Isak made waves with a string of exceptional performances for the AIK first team in 2016, leading to several big clubs chasing his signature. Dortmund ultimately beat the competition.
AIK have now been ordered to pay 350,000 kronor ($39,700) following the transfer of the 17-year-old rising star of Swedish football to the German club in January however.
The club protested that world football governing body FIFA – which approved the transfer – failed to spot the payment.
FIFA transfer rules prohibit players and clubs from making payments to agents for under-age players.
"Our experience of selling under-age players internationally is very limited and we trusted ... We'll know better next time," the club said in a statement.
Forward Isak, who turns 18 in September, has already won two caps for Sweden, scoring one goal. He has played just a few minutes with the Dortmund first team in the German Cup.